Oscillation of Second-Order Mixed-Nonlinear Delay Dynamic Equations

Oscillation of Second-Order Mixed-Nonlinear Delay Dynamic Equations

Some oscillation results for second-order nonlinear delay dynamic equations

We obtain some oscillation theorems for linear delay dynamic equations on a time scale. We illustrate the results by a number of examples. 1. Preliminary Results Consider the second order linear delay dynamic equation (1.1) L[x](t) := (r(t)x(t)) + n ∑ i=1 qi(t)x(τi(t)) = 0. We will be interested in obtaining oscillation theorems for (1.1) by comparing the solutions to a related equation without...

Oscillation criteria for second-order nonlinear neutral delay dynamic equations

In this paper we will establish some oscillation criteria for the second-order nonlinear neutral delay dynamic equation ( r(t) (( y(t)+ p(t)y(t − τ))∆)γ )∆ + f (t, y(t − δ))= 0 on a time scale T; here γ > 0 is a quotient of odd positive integers with r(t) and p(t) real-valued positive functions defined on T. To the best of our knowledge nothing is known regarding the qualitative behavior of the...

Oscillation of Second Order Delay Dynamic Equations

In this paper we establish some sufficient conditions for oscillation of second order delay dynamic equations on time scales. Our results not only unify the oscillation of second order delay differential and difference equations but also are new for q-difference equations and can be applied on any time scale. We illustrate our results with many examples.

Oscillation of Nonlinear Neutral Delay Differential Equations of Second Order

Oscillation criteria, extended Kamenev and Philos-type oscillation theorems for the nonlinear second order neutral delay differential equation with and without the forced term are given. These results extend and improve the well known results of Grammatikopoulos et. al., Graef et. al., Tanaka for the nonlinear neutral case and the recent results of Dzurina and Mihalikova for the neutral linear ...